Universe can't be infinite.

[devans99]

And you would be wrong. Here are the SHA512 checksums for each file.

...

You are still missing the point. Mathematical equations are propositions.

1 = 1 is a proposition, not an evaluation.
∞ + 1 = ∞ is a PROPOSITION, not an evaluation.

There are two ways to assert its "truth" or "falsity".

You can either derive it as a theorem from previous axioms OR you can consider it as axiomatic and then see what happens. Whether it unifies with the rest of mathematics is neither here nor there. Maybe it doesn't. So what ? If using ∞/∞ = 2 in your equation makes it agree with experiment then who cares?

Yes, you have tossed the law of non-contradiction out. But your equation works so HEY! Use it as it is. Then figure out how to fix it later.
Which is exactly what QM did: https://en.wikipedia.org/wiki/Renormalization

I said if all the bits were the same the JPEGs would be the same. The bits are different. So what's your point?

You can't derive ∞ + 1 = ∞ as a valid theorem because it implies 1 = 0
You can't use ∞ + 1 = ∞ as an axiom because it immediately leads to 1 = 0

This is starting to beg belief. In my opinion you are defending the indefensible. How can you defend 1 = 0 ?

QM uses calculus IE Potential Infinity which I don't have an issue with. It's actual infinity (from set theory) that does not exist.

[TimeSeeker]

I said if all the bits were the same the JPEGs would be the same. The bits are different. So what's your point?

The point is that you couldn't come up with a decision procedure. e.g you couldn't actually compute the answer to produce a result.

You can't derive ∞ + 1 = ∞ as a valid theorem because it implies 1 = 0
You can't use ∞ + 1 = ∞ as an axiom because it immediately leads to 1 = 0

But I can use ∞/∞ = 2 as an axiom.

This is starting to beg belief. In my opinion you are defending the indefensible. How can you defend 1 = 0 ?

I am defending pragmatism. It's all we have since neither the problem of justification, nor the problem of criterion has been addressed.

https://en.wikipedia.org/wiki/Münchhausen_trilemma

QM uses calculus IE Potential Infinity which I don't have an issue with. It's actual infinity (from set theory) that does not exist.

Special pleading.

Mathematics (like all languages) has grammar rules.

If the symbol ∞ is meaningless (invalid? doesn't exist?) then any equation that contains it is GRAMMATICALLY invalid.
Much like any equation which divides by 0 is GRAMMATICALLY invalid.

The very fact that you are willing to entertain ∞ e.g that you are willing to admit it as grammatically correct (even as a potential) means that you know how to interpret its meaning and manipulate it. You know how to compute its consequences as it interacts with other symbols in your equation. It has computable consequences - it exists in SOME context.

And since there is only one context (The Universe). You are a hypocrite

[devans99]

If the symbol ∞ is meaningless then any equation that contains it is GRAMMATICALLY invalid.
Much like any equation which divides by 0 is automatically invalid.

The symbol ∞ stands for the concept of infinity. We are trying to ascertain if that's a mathematical concept or not. All you can do is plug it into maths and see if it works. And the most basic operation possible immediately fails. So we have to conclude that infinity is not a mathematical concept.

The very fact that you are willing to entertain ∞ e.g that you are willing to admit it as grammatically correct (even as a potential) means that you know how to MANIPULATE it. You know how to compute its consequences as it interacts with other symbols in your equation. Which necessarily implies that it's context-sensitive.

You are a hypocrite

I have to discuss ∞ in english and maths... how else can one talk about it? That does not make me a hypocrite.

[TimeSeeker]

The symbol ∞ stands for the concept of infinity. We are trying to ascertain if that's a mathematical concept or not. All you can do is plug it into maths and see if it works. And the most basic operation possible immediately fails. So we have to conclude that infinity is not a mathematical concept.

We define the rules of mathematics. Including the rules for whether "it works" or doesnt.

I have to discuss ∞ in english and maths... how else can one talk about it? That does not make me a hypocrite.

Do you reject mathematical equations which contain the symbol ∞ ? Asymptotic functions e.g lim x->∞ f(x) = 1

If you don't - you are a hypocrite.

[devans99]

The symbol ∞ stands for the concept of infinity. We are trying to ascertain if that's a mathematical concept or not. All you can do is plug it into maths and see if it works. And the most basic operation possible immediately fails. So we have to conclude that infinity is not a mathematical concept.

We define the rules of mathematics. Including the rules for whether "it works" or doesnt.

I have to discuss ∞ in english and maths... how else can one talk about it? That does not make me a hypocrite.

Do you reject mathematical equations which contain the symbol ∞ ? Asymptotic functions e.g lim x->∞ f(x) = 1

If you don't - you are a hypocrite.

Not limit statements. Taking the limit as x tends to infinity can be defined purely in terms of potential infinity. The chief problem with taking a limit is that as actual infinity is never achieved (that's impossible) so a limit is by definition an approximation. So I'd suggest the use of the ~ rather than = as in:

lim 1/x as as >∞ ~ 0

Small errors like writing the above as = 0 can cause discrepancies further down the line. The use of the approximately equals sign helps to guard against such errors.

[TimeSeeker]

Not limit statements. Taking the limit as x tends to infinity can be defined purely in terms of potential infinity. The chief problem with taking a limit is that as actual infinity is never achieved (that's impossible) so a limit is by definition an approximation. So I'd suggest the use of the ~ rather than = as in:

lim 1/x as as >∞ ~ 0

Small errors like writing the above as = 0 can cause discrepancies further down the line. The use of the approximately equals sign helps to guard against such errors.

Well, you are a hypocrite.

Clearly you know how to manipulate the symbol ∞. How else did you get to the answer ~ 0?

I bet you can't write an algorithm (a PROCEDURE!) to do what you did! On an actual FINITE STATE MACHINE a.k.a a computer.

You used a heuristic

[devans99]

Not limit statements. Taking the limit as x tends to infinity can be defined purely in terms of potential infinity. The chief problem with taking a limit is that as actual infinity is never achieved (that's impossible) so a limit is by definition an approximation. So I'd suggest the use of the ~ rather than = as in:

lim 1/x as as >∞ ~ 0

Small errors like writing the above as = 0 can cause discrepancies further down the line. The use of the approximately equals sign helps to guard against such errors.

Well, you are a hypocrite.

Clearly you know how to manipulate the symbol ∞. How else did you get to the answer ~ 0?

I bet you can't write an algorithm (a PROCEDURE!) to do what you did! On an actual FINITE STATE MACHINE a.k.a a computer.

You used a heuristic

I am not a hypocrite, I used potential infinity in an expression not actual infinity. I've already explained to you the difference between potential and actual infinity once. You are clearly not too great at comprehending new ideas. I think you should re-read it. Here is the wiki page if you prefer:

https://en.m.wikipedia.org/wiki/Actual_infinity

[TimeSeeker]

I am not a hypocrite, I used potential infinity in an expression not actual infinity. I've already explained to you the difference between potential and actual infinity once. You are clearly not too great at comprehending new ideas. I think you should re-read it. Here is the wiki page if you prefer:

https://en.m.wikipedia.org/wiki/Actual_infinity

The fact that you USED it in an expression AND that you could COMPUTE the result makes you a hypocrite.
You can't compute an infinity limit on a machine with finite memory.

If you think you can - show me an algorithm. Python will do just fine.

The only way you could have gotten a result is by using a heuristic

[devans99]

I am not a hypocrite, I used potential infinity in an expression not actual infinity. I've already explained to you the difference between potential and actual infinity once. You are clearly not too great at comprehending new ideas. I think you should re-read it. Here is the wiki page if you prefer:

https://en.m.wikipedia.org/wiki/Actual_infinity

The fact that you could COMPUTE the result makes you a hypocrite.

You can't compute an infinity limit on a machine with finite memory.

If you think you can - show me your algorithm.

I can estimate the result using my intuition but that estimate is based on an understanding of potential not actual infinity so I am not a hypocrite.

The fact you can't compute infinity on a finite computer plays to my argument - infinity is impossible in maths, computing, nature and it causes common sense to rail in disgust.

If this is a simulation, then it will be finite in space and time, because an infinite computer is impossible.

[TimeSeeker]

I can estimate the result using my intuition but that estimate is based on an understanding of potential not actual infinity so I am not a hypocrite.

Intuition/heuristic. Potato potatoh.

The fact you can't compute infinity on a finite computer plays to my argument - infinity is impossible in maths, computing, nature and it causes common sense to rail in disgust.

If this is a simulation, then it will be finite in space and time, because an infinite computer is impossible.

And yet - you used the damn heuristic.

Hypocrite

USING an infinity. In potential or actual form is a performative contradiction!

You violated the halting problem.

[TimeSeeker]

This is the most precise answer I can give you on a 64 bit platform:

1/(9223372036854775807^17) = 4e-323

In [1]: import sys

In [2]: sys.maxsize
Out[2]: 9223372036854775807

In [3]: 2**63-1
Out[3]: 9223372036854775807

In [4]: 1/sys.maxsize
Out[4]: 1.0842021724855044e-19

In [5]: 1/(sys.maxsize+1)
Out[5]: 1.0842021724855044e-19

In [6]: 1/(sys.maxsize+100)
Out[6]: 1.0842021724855044e-19

In [7]: 1/(sys.maxsize**2)
Out[7]: 1.1754943508222875e-38

In [8]: 1/(sys.maxsize**17)
Out[8]: 4e-323

In [9]: 1/(sys.maxsize**18)
Out[9]: 0.0

[devans99]

Now we are not getting anywhere and not discussing the issues.

Been interesting talking though thanks.

[TimeSeeker]

Now we are not getting anywhere and not discussing the issues.

Been interesting talking though thanks.

The issue is that you COMPUTED an answer to a function that is UNCOMPUTABLE IN THEORY. How?!?

If you can compute it IN PRACTICE, but not in THEORY then you are necessarily relying on intuition/heuristics/induction NOT deduction!
You have stepped outside the bounds (violated the rules!) of logic to solve the problem.

Which is a very pragmatic thing to do when faced with an intractable problem BUT it makes you a hypocrite.

The rest of your objections (potential vs actual distinction) are just post-hoc justification for breaking the rules. Special pleading

[Greylorn Ell]

You are trying to rely on intuition instead of mathematics.

Unfortunately, that doesn't work with physics.

If actual infinity existed as a mathematical quantity, it would be larger than any other quantity. But quantity + 1 > quantity, so no such quantity can exist and actual infinity therefore does not exist.

Actual infinity is just defined axiomatically in set theory; nowhere do they prove it exists and as you see from the above, its child's play to prove it does not exist.

Look, I don't like infinities in equations any more than you do and in the conventional sense they don't exist. https://en.wikipedia.org/wiki/Renormalization

But I also don't dislike infinities any less than negative; or imaginary; or complex numbers; or zeroes! None of those exist either! And so you need to keep about a sense of pragmatism. Mathematics is a tool! Mathematical objects have useful properties.

And precisely because infinities are placeholders they could represent any real-world object that BEHAVES like an infinity behaves in the context of the equation.

Consider ∞ + ∞ = ∞. What mathematical object when added to itself results in itself?
0 + 0 = 0. So infinity behaves exactly like 0!

Or ∞ * ∞ = ∞.
1 * 1 = 1,
0 * 0 = 0

Or ∞/∞ ?

Through various hacky mathematical tricks it can either be equal to 0, 2, ∞

∞ / ∞ = 0 this is new. No other mathematical object behaves this way.
∞ / ∞ = 2 so is this. Nothing divided by itself produces 2!

Anything divided by itself produces 1 (except 0).
But if you are familiar with mathematics you would reconise these as round-up and round-down errors.

∞ / ∞ = ∞ is the same as 1 / 1 = 1

And so "infinity" is a rather ambiguous mathematical object!

You need some sense of real-world behaviorism when doing mathematics.

No, nitwit. 0 does not behave like infinity. 0 + 9 = 9 whereas infinity + 9 (or anything else) = infinity.

You exemplify the problem with this forum, in the person of one of the many philosopher wanna-be's who pretend to know more than they do. For shame on the lot of you and your pretentious ilk.

[TimeSeeker]

No, nitwit. 0 does not behave like infinity. 0 + 9 = 9 whereas infinity + 9 (or anything else) = infinity.

You exemplify the problem with this forum, in the person of one of the many philosopher wanna-be's who pretend to know more than they do. For shame on the lot of you and your pretentious ilk.

No, you fossil. Just because you did physics a century ago doesn't mean you have a clue what you are talking about either.
https://en.wikipedia.org/wiki/Curry–How ... espondence

∞ + 9 = ∞ is a AXIOMATIC truth.

That kind of shit stopped being relevant 300 years ago.
One person can ASSUME it's true, another person can ASSUME it is not!
Neither will run into any contradictions.

Now lets try this exercise in Lambda calculus/Type theory.

∞ + 9 = ∞ is a PROPOSITION!

True/false is a foreign notion. A proposition is either proven or not! So IF you can write an algorithm which evaluates the assertion THEN it is proven to be mathematically valid. And guess what. I CAN!

IF ∞ + 9 = ∞ THEN X + 0 = X ISOMORPHIC.

That is to say ANY equation containing ∞ makes all other numbers BEHAVE like zero. Context and interpretation!

And so ∞ + 9 + 10000 + 1000000000 = ∞
Because 9, 10000 and 10000 BEHAVE like 0 in context of ∞ .

Now IF you can tell the rest of us what you MEAN by "infinity" that would be great.

e.g define its TYPE in Lambda calculus. But you can't

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. It makes a close link between model theory that deals with what is true in different models, and proof theory that studies what can be formally proven in particular formal systems.

You are a peon like the rest of them "philosophers" who bow down to axiomatic truth.

Proofs compute.

If you REALLY meant infinity (as in ACTUAL infinity) you cannot evaluate ∞ + 9 but since you have gone ahead and evaluated (A.K.A COMPUTED) it. Apparently you think there is a way to do it.